SUBMITTED TO: sir sajid presentation on application of secant method April 16‚ 2013 MCS 1st sem ------------------------------------------------- ROLL # 31 to 40 SECANT METHOD * The Secant command numerically approximates the roots of an algebraic function‚ f‚ using a technique similar to Newton’s method but without the need to evaluate the derivative of function. * Given an expression f and an initial approximate a‚ the Secant command computes a sequence‚ =‚ of approximations
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Task #3: Abstract Algebra Competency 210.4.2: Groups & Competency 210.4.4: Fields Jennifer Moore Western Governor’s University Part A: The image below is the fifth roots of unity. Using these fifth roots of unity and de Moivre’s formula to verify that the fifth roots of unity form a group under complex multiplication. de Moivre’s formula is z^k=cos(2πk/n)+isin(2πk/n)‚k=0‚1‚2‚…‚n-1 (Nicodemi‚ 2006) for the 5th roots unity of n=5. The following show the fifth roots of unity using
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Name: Date: Graded Assignment Checkup: Graphing Polynomial Functions Answer the following questions using what you’ve learned from this unit. Write your responses in the space provided‚ and turn the assignment in to your instructor. For problems 1 – 5‚ state the x- and y-intercepts for each function. 1. x-intercept: (0‚ 0)‚ (-4‚ 0)‚ (0‚ 0) y-intercept: (0‚ 0) 2. x-intercept: (1‚ 0) (0‚ 0) (-4‚ 0) y-intercept: (0‚ 4) 3. x-intercept: (-1‚ 0) (0‚ 0) (0‚ 0) y-intercept: (0‚ 0) 4
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Roots Ac‚Acr Meaning sharp Words Acrimonious Meaning bitter‚ caustic Acerbity Acidulate bitterness of temper to make somewhat acid or sour Aev‚Ev age‚era Primeval Coeval Medieval or Mediaeval of the first age of the same age or era of the middle ages Agog Leader Demagogue pedagogue false leader of people teacher (leader of children) Agaro to discuss or speak Panegyric formal praise Ali another Alias alienate assumed (another)
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Summary of Convergence and Divergence Tests for Series TEST nth-term Geometric series p-series Integral SERIES ∑ an CONVERGENCE OR DIVERGENCE Diverges if lim n→∞ an ≠ 0 (i) Converges with sum S = (ii) Diverges if r ≥ 1 1 p COMMENTS Inconclusive if lim n →∞ an = 0 Useful for the comparison tests if the nth term an of a series is similar to arn-1 Useful for the comparison tests if the nth term an of a series is similar to 1/np The function f obtained from an = f ( n ) must be continuous‚ ∑
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About the Author Tony Crilly is a freelance writer‚ having previously taught at the University of Michigan‚ the City University in Hong Kong‚ Middlesex University and the Open University. His principal research interest is the history of mathematics‚ and he has written and edited many works on fractals‚ chaos and computing. He is the author of the acclaimed biography of the English mathematician Arthur Cayley and popular maths book How Big is Infinity? Reflection 50 Ideas You Really Need To Know
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Contents Pages OBJECTIVES 3 ACKNOWLEDGEMENTS 4 INTRODUCTION 5 PART 1 6 PART 2 7-12 PART 3 13-17 FURTHER EXPLORATION 18-19 REFLECTION 20-21 OBJECTIVES We students taking Additional Mathematics are required to carry out a project while we are in Form Five. This project can be done in groups or individually‚ but each of us is expected to submit an individually report. Upon completion of the Additional Mathematics Project Work‚ we are to gain valueable experiences and able to:
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HIPPARCHUS (c 190 – c120 BC) Hipparchus was a Greek astronomer‚ mathematician and geographer. Surprisingly little is known about his early life. He was most certainly born in Nicaea‚ Bithynia‚ (which is now known as Iznik in Turkey)‚ around 190 BC. Most of what we do about him comes from the books of other scholars who came after him‚ such as Ptolemy and Strabo. It seems likely that Hipparchus studied in Alexandria but spent his later life in Rhodes. Strabo‚ another Greek geographer writing about
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| | (0‚ ∞)Question 8 Find the largest open interval(s) where the function is Increasing y = x4 - 18x2 + 81Answer | | (-∞‚ 0) | | | (-3‚ 0) | | | (-3‚ 3) | | | (3‚ ∞) | Question 9 S(x) = -x3 + 6x2 + 288x + 4000‚ 4 ≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn‚ where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.Answer | | 8°C | | | 20°C | | | 4°C | | | 12°C |
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EEE233 (SEM2-2012/13) TUTORIAL 1: PARTIAL DIFFERENTIAL EQUATIONS 1. Solve the following equations a) ∂2u∂x2=24x2(t-2)‚ given that at x=0‚ u=e2tand ∂u∂x=4t. b) ∂2u∂x∂y=4eycos2x‚ given that at y=0‚ ∂u∂x=cosx and at x=π‚ u=y2. 2. A perfectly elastic string is stretched between two points 10 cm apart. Its centre point is displaced 2 cm from its position of rest at right angles to the original direction of the string and then released with zero velocity. Applying
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